Mathematical model of the first-order phase transition due to fluctuation of thermodynamical parameters presented as system of equations of mathematical physics in partial derivatives of the Kolmogorov-Feller and Einstein-Smolukhovskyi and stochastic differential equations of Ito -Stratonovich. Computer simulation study of the nonlinear stage of nucleation can be used in the powders synthesis and thin films of silicon carbide. Model processes of condensation and crystallization, as well as vacancy-gas defects clustering are presented as superposition of Wiener random processes such as stochastic diffusion in phase space cluster sizes of nuclei and spatial their Brownian motion, which are stimulated by long-range self-consistent potential indirect elastic interaction of the clusters of nuclei on the surface and in the volume of the substrate. The effective algorithms for stochastic differential equations with nonlinear functional-coefficients worked out. Kinetic functions of distribution clusters of nuclei from size and spatial coordinates for the conditions of model numerical experiments are calculated. The stressed state of crystal lattice which is proceeded to a solid phase epitaxy thin film of silicon carbide in a silicon substrate has been studied. The results can be used to optimize the coating processes, to control of uniformity and application speed deposition of fine films.